Question

Determinação da derivada 3x+5/x-1

Answer 1

$f(x)=\dfrac{3x+5}{x-1}$

Derivando pela Regra do Quociente:

$\dfrac{df}{dx}(x)=\dfrac{d}{dx}\!\left(\dfrac{3x+5}{x-1} \right )\\\\\\ \dfrac{df}{dx}(x)=\dfrac{\left[\frac{d}{dx}(3x+5) \right ]\cdot (x-1)-(3x+5)\cdot \left[\frac{d}{dx}(x-1) \right ]}{(x-1)^2}\\\\\\ \dfrac{df}{dx}(x)=\dfrac{3\cdot (x-1)-(3x+5)\cdot 1}{(x-1)^2}\\\\\\ \dfrac{df}{dx}(x)=\dfrac{\diagup\!\!\!\!\! 3x-3-\diagup\!\!\!\!\!3x-5}{(x-1)^2}\\\\\\ \boxed{\begin{array}{c}\dfrac{df}{dx}(x)=-\,\dfrac{8}{(x-1)^2} \end{array}}$